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Making Fractions Fun, SMALLab Style

Finally coming up for air and getting a little time to blog about some interesting stuff I've been a part of. Just to get started, I wanted to show off a video my colleague Claudio Midolo shot of our fraction game in SMALLab, which we've provisionally dubbed "FracAttack".

Fear of a Black Swan

Colleen Macklin forwarded Kyle Li and I this excellent post on Raph Koster's blog about the Ludic Fallacy. In essence, the ludic fallacy is when people "mistake the model for reality." Koster's take was that this can drive younger people, who have been raised on the lessons in games, to be too likely to assume that real world choices hew closely to those provided to them in games. Koster's view of the consequences:

Recently I had a discussion with a management and leadership consultant, and we were discussing the generational characteristics of Millenials versus Gen X in the workforce, and we were talking about how a gamer mentality may have affected the way Gen Y behaves in the workplace: more likely to follow the rules, more likely to work in teams, more needful of reassurance, less creative and risk-taking, less likely to see the full scope of irreversible consequences of a choice, and less likely to see things in shades of gray. In a way, these sound like thinking trained by games.

The ludic fallacy comes from the work of Nassim Nicholas Taleb who also popularized the term "black swan". The Black Swan theory describes events that are highly improbable and have a large impact (and that we, retrospectively, try to assume were predictable). Black Swans are particularly dangerous for people who have been trained to think they don't exist (frankly, that's pretty much all of us.) As Taleb writes in his book:

...we can easily trigger Black Swans thanks to aggressive ignorance-like a child playing with a chemistry kit.

By assuming that we can predict outliers (we can't) and that these events they precipitate are of no great consequence (they are), we allow ourselves to be lulled into thinking that our lives are run in the same contained set of rules that might apply even in an advanced game simulation.

The cure? My read on Koster is that we should consider throwing Black Swans into educational games... or all games. By creating a set of circumstances where student players know that catastrophic events are possible (if unlikely), we will, hopefully, encourage kids (and adults) to think more conservatively and more long-term when making their choices. Having to plan for the 100-year flood (or the 500-year flood) makes the player prepare for eventualities that they may never experience themselves. The student players are therefore made to consider their game worlds as places where the rules apply only 99% (or more) of the time--enough that they can't totally rely on them as models for reality.

The catch? Randomness is not fun. Sort of. Nick Fortugno and others have taught me there are appropriate uses of randomness. For example, randomizing the terrain of the game tends to work. Players must then make their own choices on this playing field. But randomizing the choices themselves usually is a miserable failure. Try playing a game where all your moves are based solely on the roll of a die, like Candy Land or Chutes and Ladders. They're awful, unless you're a four year old.

It seems, then, that the Black Swans have to be carefully inserted into games in the form of "terrain" changes--the sudden appearance of ridiculously powerful enemies, the total elimination (or tripling) of one's resources, the widespread reformatting of a game's map. They effect the field on which the player makes choices, without inhibiting or supplementing the ability to make them in the first place. The resulting choices will be difficult and victories will be rare and hard won, but the core of gaming remains.

These events also need to be real outliers, going beyond the single super-powerful card in the deck (which savvy players would be able to predict). For example, the "Your Parents Never Met" card in Chrononauts is an okay example, but, I think, it'd have to be even more unlikely than it is now. You should be aware, in the back of your mind, that something truly awful can happen down the line, but you shouldn't be able to count cards or analyze models well enough to predict it.

Will this work? Will it cure the Gen Ys (or, as they're known in Taiwan, "strawberries") of their reliance on limited game rules in real life? Will it still leave them with their confidence, their tactical good sense, their teamwork--positive consequences of game training, according to Koster? I dunno. But it's worth a shot. And, who knows, we might even... WAAARGH! THREE-HEADED ALIENS ARE ATTACKING!

Sonic Slope and the Coordinate Dance

Here are a few more videos from last week's session with ASU. The first is a math game for two players to help students learn about slope through physical and audio interaction. The players can listen to the change in coordinates and then try to determine the right slope based on their positions in three-dimensional space.

There are some issues here with finding the right location for the balls that will prompt some work in the future. Knowing, for example, that you are "on" the right point in the Z-axis may require different kinds of audio cues. One idea we've had is a kind of sonic prompt that fades out when you've hit your mark, but gets louder and louder as you approach the boundary between two integers. This, we hope, will help people visualize where the number 2 and 3 are, rather than floating on the boundary between them and continually triggering the audio sample.

The next video is an improvised dance that the students can choreograph as they each try to reach their X and Y coordinates. This is a variation on the "Coordinate Game" that we had developed the day before. Hopefully, students will get an embodied sense of how the Cartesian system works as they move along in their algebra/geometry units.

It's not quite a game yet, but there's something really fun and compelling about making your own art work (a dance piece) that corresponds to your math assignment.

The Coordinate Game

This is simple game we created as part of the SMALLab workshop here at Parsons. It's for teaching middle-school students how to figure out coordinates on a projected grid.

Each player takes their own origin as 0,0 and must reach the goal marker laid down by the teacher. The first player to correctly call out the coordinates of her or his goal marker wins.

Congrats to Christopher for his mad math dancing skills!

Idea Sketch - Sine Wave

Idea Sketch - Sine Wave

A mock up of an applet that would let designers explore the possibilities of a sine wave graphically.

Design Challenge #4: Math Cookbook


Design a lecture or instructional piece for something missing from the MFADT curriculum.


Teaching graduate design students the kinds of math they need to do interesting graphics, games, and other computational designs.
Parsons MFADT students.
In class or in lab project work.
What is the best and most useful way to provide Parsons MFADT students with the kinds of math that they need with out getting bogged down in details that do not relate to their needs or work?

Copyright Mike Edwards 2006-2009. All content available under the Creative Commons Attribution ShareAlike license, unless otherwise noted.

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